Solve a quadratic with trigonometric values in degrees

[axekick]

I'm trying to solve for x in the function:

-16.1(15/cos(x))^2 + 800*sin(x)*(15/cos(x)) =2000

It should be a "zeros" problem but my HP50g calculator is making me put it in radians mode and won't solve the equation in degrees. Does anyone know what I'm doing wrong? I can't find an example like this anywhere.

[Albert Chan]

Hi, axekick

I tried this in emu48, degree mode, but cannot reproduce your problem.

[Orange] [7] for Num. Slv
Pick 1. Solve equation [Enter]

Eq: '-16.1*(15/COS(X))^2 + 800*SIN(X)*(15/COS(X)) - 2000'

X: 0 [SOLVE] → 29.4603650656
X: 60 [SOLVE] → 70.0019571424

[axekick]

Thank you for trying that. I still can't get the answer I'm looking for. Also, when doing it that way, does the calculator write a value to the variable 'X' that then needs to be cleared?

[Moggul]

I duplicated Albert Chan's operations on my HP48G+ and get the same results.

[axekick]

I did it like that again and it worked. However, I was hoping i could just solve for zeros using "ZEROS" but I get a prompt to switch to radians and it doesn't perform the calculations unless I do. I suppose I'll just have to learn to use the equation solver. Thanks for the help!

[axekick]

I'm about to give up on this calculator. I've used it for quite a few classes but usually my problems had numbers that worked out better and this calculator is not going to work for me on exam day if it won't solve these seemingly simple equations. I'm on a new problem now, again I know what the answer is from the solution manual but I can't get to it with my calculator and I've spent hours trying to figure out how. We're not even to the hard stuff yet and I'm scared! The algebra problem I'm stuck on is:

d*cos(30) = 25*sqrt(d/9.81)

The solution is d=84.95. I can't even get my calculator to give me a solution. I've tried solve, solvevx (using x as my variable), zeros and the equation solver with no luck.

[Carsen]

The past replies are pointing you in the right direction. The equation solver is the best tool for the job on the 50g because your problem is asking for a numerical answer. If the equation solver doesn't work or spits out an error, enter a guess for the variable you are solving for and try again. It will find the answer closest to that guess.

However...

You can use SOLVE, SOLVEVX, & ZEROS to find the solutions as well. These functions are known as CAS (computer algebraic system) functions. Typically, to use CAS functions...

1. The calculator needs to be in radian mode
2. The calculator needs to be in exact mode. See the equals sign by R= in the header? You need that = sign.
3. The equation must have no decimal points in them. If they have decimal points in them, press [white shift] [ 6 ] REWRITE [ NXT] ->Q. This command will take the whole equation & convert decimals to fractions.
   

In order to understand the above, here are the steps used to solve your problem d*cos(30) = 25*sqrt(d/9.81) with the SOLVE command. I am assuming you are in RPN mode.

1. Look at the image attached & make sure the 50g's header has RAD & '=' displayed.
2. Type 'D*COS(30) = 25*SQRT(D/9.81)' and press ENTER
3. Now press [white shift] [ 6 ] REWRITE [ NXT ] ->Q.
4. Type 'D'. Then use the PURGE command.
5. Type 'D'. Then use the SOLVE command. You should get { D=62500/(981*COS(30)^2) D=0 }
6. Press [white shift] [ EVAL ] TYPE OBJ->
7. Get D=62500/(981*COS(30)^2) on level 1 of the stack & put the 50g in degree mode
8. Press [down arrow] [down arrow] [backspace] [backspace] [backspace] [orange shift] [ENTER]. It should say 84.9473326539.
   

A lot of work huh! This really shows that the equation solver is the best tool for the job. This calculator is hard to learn BUT once you get it, you'll cut through problems like a hot knife through butter.

If you have questions, let me know.

[Mark Hardman]

(01-28-2020 05:16 AM)Carsen Wrote:  A lot of work huh!

Most of that work could be eliminated if the OP recognized that cos(30) = √3/2. From there, it is only a minor mental effort to come up with d = 2500/(3*9.81). Why on earth would you need a CAS to solve that?

IMO, this is an example of the dangers of symbolic calculators in the classroom.

I know... "OK, Boomer"...

[Albert Chan]

(01-28-2020 05:51 AM)Mark Hardman Wrote:  Most of that work could be eliminated if the OP recognized that cos(30) = √3/2. From there, it is only a minor mental effort to come up with d = 2500/(3*9.81). Why on earth would you need a CAS to solve that?

Same with OP

Let t = tan(x), the equation is just quadratics: -16.1*225*(1+t²) + 800*15*t = 2000
Remember that t = tan(x) have period of Pi = 180°, x have 4 solutions

d*cos(30) = 25*sqrt(d/9.81) is also a quadratics (of √d), d thus have 2 solutions.

[axekick]

Thanks everyone, especially you Carsen. That is a good explanation of how the CAS get used. I know this problem shouldn't need the CAS or any fancy calculator to solve this problem but I can't spend my meek brain power on solving the algebra when exam day is here. I spend too much time on it and if I have a tool in front of me that'll save me that time I just need to know how to use it on whatever comes up.

How do you get multiple answers from the equation solver in the case that there are multiple answers?

[Massimo Gnerucci]

(01-28-2020 02:15 PM)axekick Wrote:  (...) I can't spend my meek brain power on solving the algebra when exam day is here.(...)

The Times They Are a-Changin'

:)